review of lecture 3 data type and declaration integer e.g., a, b, c real e.g., x, y, z, w logical...

Review of lecture 3 Data type and declaration

INTEGER E.g., a, b, c

REAL E.g., x, y, z, w

LOGICAL COMPLEX CHARACTER

Examples: INTEGER::a=1,b=-5,c=5 REAL::x=2.0

Review of lecture 3 (cont.)

Arithmetic expressions E.g., 5 + 2 *3 E.g., b**2 – 4*a*c

It has a value by itself E.g. expression: 5 + 2*3 has a value of 11

Review of lecture 3 (cont.)

Evaluating Complex Expressions Precedence Associativity (For expressions having operators with the

same precedence).

operators Precedence associativity

() 1 Left to right

** 2 Right to left

*, / 3 Left to right

+, - 4 Left to right

Review of lecture 3 (cont.)

Mixed Mode Expressions If one operand of an arithmetic operator is INTEGER and the other is

REAL the INTEGER value is converted to REAL the operation is performed the result is REAL1 + 2.5 3.5 1/2.0 0.5 2.0/8 0.25 -3**2.0 -9.04.0**(1/2) 1.0 (since 1/2 0)3/5 * 5.0 0.0 (since 3/5 0)

Review of lecture 3 (cont.)

Statements Assignment statement:

Variable = expression

e.g., b = -5

(never the other way around, 5=b is not valid!)

General statement:INTEGER a, b, c

write (*,*) ‘Hello world!’

Selection in FORTRAN

Lecture 4

By Nathan Friedman and Yi Lin

Jan 16, 2007

Roots of a Quadratic (again)! --------------------------------------------------! Solve Ax^2 + Bx + C = 0 given B*B-4*A*C >= 0! --------------------------------------------------PROGRAM QuadraticEquation IMPLICIT NONE REAL :: a, b, c, d, root1, root2

! read in the coefficients a, b and c WRITE(*,*) "A, B, C Please : " READ(*,*) a, b, c

! compute the square root of discriminant d d = SQRT(b*b - 4.0*a*c)

! solve the equation root1 = (-b + d)/(2.0*a) ! first root root2 = (-b - d)/(2.0*a) ! second root

! display the results WRITE(*,*) "Roots are ", root1, " and ", root2 END PROGRAM QuadraticEquation

Run Time Error

We assumed that the discriminant was positive

What if it wasn’t?We would get an error when we run the program and

attempt to compute the square root and the program would abort

What should we do?Avoid trying to perform an illegal operation by branching

around it -- use a selection control structure

Quadratics example

d=b*b – 4.0*a*c

D>=0.0

Calc root1, root2

Ouput “no real roots!”

.TRUE. .FALSE.

end

IF-THEN-ELSE-END IF

Used to select between two alternative sequences of statements.

They keywords delineate the statement blocks.Syntax: IF (logical-expression) THEN first statement block, s_1 ELSE second statement block, s_2 END IF

IF-THEN-ELSE-END IF

Semantics:• Evaluate the logical expression. It can have

value .TRUE. or value .FALSE.• If the value is .TRUE., evaluate s_1, the first block of

statements• If the value is .FALSE., evlaluate s_2, the second block

of statements• After finishing either s_1 or s_2, execute the statement

following the END IF

Roots of Quadratic – v.2! ----------------------------------------------------------------! Solve Ax^2 + Bx + C = 0 given B*B-4*A*C >= 0 ! ---------------------------------------------------------------- PROGRAM QuadraticEquation IMPLICIT NONE REAL :: a, b, c, d, root, root2 ! read in the coefficients a, b and c

WRITE(*,*) "A, B, C Please : " READ(*,*) a, b, c

!compute the square root of discriminant d d = b*b - 4.0*a*c IF (d >= 0.0) THEN ! is it solvable? d = SQRT(d) root1 = (-b + d)/(2.0*a) ! first root root2 = (-b - d)/(2.0*a) ! second root WRITE(*,*) "Roots are ", root1, " and ", root2 ELSE ! complex roots WRITE(*,*) "There is no real roots!" WRITE(*,*) "Discriminant = ", d END IFEND PROGRAM QuadraticEquation

Logical Expressions

Relational operators return result of .TRUE. or .FALSE<, <=, >, >=, ==, /=

Relational operators are of lower precedence than all arithmetic operators2 + 7 >= 3 * 3 .TRUE.

There is no associativitya < b < c illegal

Note that == means “is equal to” but = means “assign the value on the right”

Data Type Logical

Where do .TRUE. and .FALSE. come from? FORTRAN has a LOGICAL data type, just like

it has INTEGER and REAL types We can declare variables to be of this type and

assign values to them

LOGICAL :: positive_x, condition

condition = .TRUE.

positive_x = x > 0

Is Number Even or Odd?

IF (MOD(number, 2) == 0) THEN

WRITE(*,*) number, " is even"

ELSE

WRITE(*,*) number, " is odd"

END IF

MOD(a, b): Intrinsic function, returning the remainder of a/b

Find Absolute Value

REAL :: x, absolute_x x = ..... IF (x >= 0.0) THEN absolute_x = x ELSE absolute_x = -x END IF WRITE(*,*) “The absolute value of “,& x, “ is “, absolute_x Note the use of & to indicate “continue on next line”

Which value is smaller?

INTEGER :: a, b, min READ(*,*) a, b IF (a <= b) THEN min = a ELSE min = b END IF Write(*,*) “The smaller of “, a, & “ and “, b, “ is “, min

IF-THEN-END IF

The IF-THEN-ELSE-END IF form allows us to choose between two alternatives

There is another simpler selection mechanism that allows us to choose whether or not to perform a single block of actions

We either perform the actions and go on, or skip them and go on

IF-THEN-END IF

Syntax:IF (logical expression) THEN

block of statementsEND IF

Semantics:1. Evaluate the logical expression2. If it evaluates to .TRUE. execute the block of statements and

then continue with the statement following the END IF3. If the result is .FALSE. skip the block and continue with the

statement following the END IF

Examples of IF-THEN-END IFabsolute_x = x IF (x < 0.0) THEN absolute_x = -x END IF WRITE(*,*) "The absolute value of ", x, " is ", absolute_x

------------------------------------------------- INTEGER :: a, b, min READ(*,*) a, b min = a IF (a > b) THEN min = b END IF Write(*,*) "The smaller of ", a, " and ", b, " is ", min

Logical IF

An even simpler form is sometimes useful

Syntax:IF (logical expression) single-statement

Semantics: equivalent toIF (logical expression) THEN

single-statement

END IF

Examples of Logical IFabsolute_x = x IF (x < 0.0) absolute_x = -x WRITE(*,*) "The absolute value of ", x, & " is" ,"absolute_x

------------------------------------------------- INTEGER :: a, b, min READ(*,*) a, b min = a IF (a > b) min = b Write(*,*) "The smaller of ", a, " and ", b, & " is ", min

IF-THEN-ELSE IF-END IF

IF-THEN-ELSE-ENDIF can only handle processes which have two options.

Sometimes we have more than 2 options for one process.

For example, in the quadratic equation problem, there may be two equivalent roots. We want to detect this and complex roots at the same time.

Solution: put another IF-THEN-ELSE-ENDIF in the ELSE block

IF-THEN-ELSE IF-END IF

SyntaxIF (logical-expression1) THEN

first statement block, s_1 ELSE

IF (logical-expression2) THEN second statement block, s_2 ELSE third statement block, s_3 END IFEND IF

IF-THEN-ELSE IF-END IF

Semantics:• Evaluate the logical expression 1. It can have value .TRUE. or

value .FALSE.• If the value is .TRUE., evaluate s_1, the first block of statements• If the value is .FALSE.,

evaluate the logical expression 2. It can have value .TRUE. Or value .FALSE.

If the value is .TRUE., evaluate s_2, the second block of statements If the value is .FALSE., evaluate s_3, the third block of statements After finishing either s_2 or s_3, execute the statement following

ENDIF• After finishing either s_1 or s_2 or s_3, execute the statement

following the END IF

Roots of Quadratic v.3! ---------------------------------------------------! Solve Ax^2 + Bx + C = 0 given B*B-4*A*C >= 0 ! Detect complex roots and repeated roots.! ---------------------------------------------------PROGRAM QuadraticEquation IMPLICIT NONE

REAL :: a, b, c, d, root1, root2! read in the coefficients a, b and c READ(*,*) a, b, c

! comute the discriminant d d = b*b - 4.0*a*c IF (d > 0.0) THEN ! distinct roots? d = SQRT(d) root1 = (-b + d)/(2.0*a) ! first root root2 = (-b - d)/(2.0*a) ! second root WRITE(*,*) 'Roots are ', root1, ' and ', root2 ELSE IF (d == 0.0) THEN ! repeated roots? WRITE(*,*) 'The repeated root is ', -b/(2.0*a) ELSE ! complex roots WRITE(*,*) 'There is no real roots!‘ WRITE(*,*) 'Discriminant = ', d END IF END IFEND PROGRAM QuadraticEquation

IF-THEN-ELSE IF-END IF You can put IF-THEN-ELSE IF-ENDIF within ELSE block

repeatedly.IF (logical-expression1) THEN first statement block, s_1ELSE

IF (logical-expression2) THEN second statement block, s_2 ELSE IF-THEN-ELSE IF-ENDIF END IFEND IF

There is a concise way to do this.

IF-ELSEIF-ELSE-ENDIF

syntaxIF (logical expression 1) THEN

block 1ELSEIF (logical expression 2) THEN

block 2 ... ELSEIF (logical expression N-1) THEN

block N-1[ELSE

block N] ENDIF

IF-ELSEIF-ELSE-ENDIF

Semantics First evaluate the logical expression 1. It can have value .TRUE. or

value .FALSE. If the value is .TRUE., evaluate the first block of statements. If the value is .FALSE., evaluate the logical expression 2. It can have

value .TRUE. or value .FALSE. If the value is .TRUE., evaluate the second block of statements. Repeat this until all logical expressions have been evaluated. If none of them are .TRUE., evaluate block N within ELSE and

ENDIF. After that, execute the statement following the ENDIF

Roots of Quadratic v.4---------------------------------------------------! Solve Ax^2 + Bx + C = 0 given B*B-4*A*C >= 0 ! Detect complex roots and repeated roots.! ---------------------------------------------------PROGRAM QuadraticEquation IMPLICIT NONE

REAL :: a, b, c, d, root1,root2! read in the coefficients a, b and c READ(*,*) a, b, c! compute the discriminant d

d = b*b - 4.0*a*c IF (d > 0.0) THEN ! distinct roots? d = SQRT(d) root1 = (-b + d)/(2.0*a) ! first root root2 = (-b - d)/(2.0*a) ! second root WRITE(*,*) 'Roots are ', root1, ' and ', root2 ELSEIF (d == 0.0) THEN ! repeated roots? WRITE(*,*) 'The repeated root is ', -b/(2.0*a) ELSE ! complex roots WRITE(*,*) 'There is no real roots!‘ WRITE(*,*) 'Discriminant = ', d END IFEND PROGRAM QuadraticEquation

Example in previous midtermsPROGRAM X

IMPLICIT NONELOGICAL :: A,B,CINTEGER :: I,J,KI = 5/2+2.5J= 13.0/3.0 + 0.66K = 5A = (I==J)B = (K > J)C = (K==I)WRITE (*,*) A, B, C

END PROGRAM

1- T T T

2- T F T

3- T F F

4- F T F

5- None of the above

Complex Logical Expressions

In addition to relational operators, more complex logical expressions can be formed using logical operators

The Logical Operators listed in order of decreasing precedence are:.NOT..AND..OR..EQV., .NEQV.

The precedence of all logical operators is lower than all relational operators

They all associate from left to right except .NOT.

High

Low

Logical operator: .AND. (&&)

Examples (2>1) .and. (3<4) .TRUE. (2>1) .and. (3>4) .FALSE. (2<1) .and. (3<4) .FALSE. (2<1) .and. (3>4) .FALSE.

.TRUE. .FALSE.

.TRUE. .TRUE. .FALSE.

.FALSE. .FALSE. .FALSE.

<exp1> .AND. <exp2>

exp2exp1

<exp1> && <exp2>

.TRUE. .FALSE.

.FALSE. .FALSE.

Logical operator: .OR. (||)

Examples (2>1) .OR. (3<4) .TRUE. (2>1) .OR. (3>4) .TRUE. (2<1) .OR. (3<4) .TRUE. (2<1) .OR.

(3>4) .FALSE.

.TRUE. .FALSE.

.TRUE. .TRUE. .TRUE.

.FALSE. .TRUE. .FALSE.

<exp1> .OR. <exp2>

exp2exp1

<exp1> || <exp2>

Logical operator: .EQV.

Examples (2>1) .EQV. (3<4) .TRUE. (2>1) .EQV. (3>4) .FALSE. (2<1) .EQV. (3<4) .FALSE. (2<1) .EQV. (3>4) .TRUE.

.TRUE. .FALSE.

.TRUE. .TRUE. .FALSE.

.FALSE. .FALSE. .TRUE.

<exp1> .EQV. <exp2>

exp2exp1

Logical operator: .NEQV.

Examples (2>1) .NEQV. (3<4) .FALSE. (2>1) . NEQV. (3>4) . TRUE. (2<1) . NEQV. (3<4) .TRUE. (2<1) . NEQV. (3>4) .FALSE.

.TRUE. .FALSE.

.TRUE. .FALSE. .TRUE.

.FALSE. .TRUE. .FALSE.

<exp1> .NEQV. <exp2>

exp2exp1

Logical operator: .NOT.

Examples .NOT. (2<1) .TRUE. .NOT. (2>1) .FALSE. .TRUE. .FALSE.

.FALSE. .TRUE.

.NOT. <exp>

exp

Examples

Suppose we have the declaration:INTEGER :: age=34, old=92, young=16

What is the value of the following expressions? age /= oldage >= youngage == 62 age==56 .and. old/=92 age==56 .or. old/=92 age==56 .or. .not.(old/=92).not. (age==56 .or. old/=92)

Another Example

Suppose the integer variable, n has value 4. n**2 + 1 > 10 .AND. .NOT. n < 3

4**2 + 1 > 10 .AND. .NOT. 4 < 3 [4**2] + 1 > 10 .AND. .NOT. 4 < 3 16 + 1 > 10 .AND. .NOT. 4 < 3 [16 + 1] > 10 .AND. .NOT. 4 < 3 17 > 10 .AND. .NOT. 4 < 3 [17 > 10] .AND. .NOT. 4 < 3 .TRUE. .AND. .NOT. 4 < 3 .TRUE. .AND. .NOT. [4 < 3] .TRUE. .AND. .NOT. .FALSE. .TRUE. .AND. [.NOT. .FALSE.] .TRUE. .AND. .TRUE. .TRUE.

Example in the final of Fall 2006What is the output of the following

Fortran program?PROGRAM exam IMPLICIT NONE LOGICAL :: X,Y INTEGER :: I=2, J=3 REAL :: A=5.0,B=9.0 X = (A/I) < (B/J) Y = (J/I) == (B/A) X = X .AND. Y Y = X .OR. Y WRITE (*,*) X, YEND PROGRAM exam

a). T Fb). T Tc). F Td). F Fe). The program does not

compile